More by Victor Pambuccian

Abstract

Reverse analyses of three proofs of the Sylvester-Gallai
theorem lead to three different and incompatible axiom systems.
In particular, we show that proofs respecting the purity of the
method, using only notions considered to be part of the statement
of the theorem to be proved, are not always the simplest, as they
may require axioms which proofs using extraneous predicates do not
rely upon.